probable cause

Probable cause is a requirement found in the Fourth Amendment that must usually be met before police make an arrest, conduct a search, or receive a warrant. Courts usually find probable cause when there is a reasonable basis for believing that a crime may have been committed (for an arrest) or when evidence of the crime is present in the place to be searched (for a search). Under exigent circumstances, probable cause can also justify a warrantless search or seizure. Persons arrested without a warrant are required to be brought before a competent authority shortly after the arrest for a prompt judicial determination of probable cause.

Law.cornell.edu

https://www.law.cornell.edu/wex/probable_cause